Multiplying Matrices Using dgemm

Intel MKL provides several routines for multiplying matrices. The most widely used is the `dgemm` routine, which calculates the product of double precision matrices:

The `dgemm` routine can perform several calculations. For example, you can perform this operation with the transpose or conjugate transpose of A and B. The complete details of capabilities of the `dgemm` routine and all of its arguments can be found in the `?gemm` topic in the Intel Math Kernel Library Reference Manual.

Use dgemm to Multiply Matrices

This exercise demonstrates declaring variables, storing matrix values in the arrays, and calling `dgemm` to compute the product of the matrices. The arrays are used to store these matrices:

The one-dimensional arrays in the exercises store the matrices by placing the elements of each column in successive cells of the arrays.

Note

The Fortran source code for the exercises in this tutorial is found in <install-dir>\Samples\en-US\mkl\tutorials.zip (Windows* OS), or <install-dir>/Samples/en-US/mkl/tutorials.zip (Linux* OS/OS X*).

Although Intel MKL supports Fortran 90 and later, the exercises in this tutorial use FORTRAN 77 for compatibility with as many versions of Fortran as possible.

After you unzip the tutorials.zip file, the Fortran source code can be found in the mkl_mmx_f directory, and the C source code can be found in the mkl_mmx_c directory.

```* Fortran source code is found in dgemm_example.f

PROGRAM   MAIN

IMPLICIT NONE

DOUBLE PRECISION ALPHA, BETA
INTEGER          M, K, N, I, J
PARAMETER        (M=2000, K=200, N=1000)
DOUBLE PRECISION A(M,K), B(K,N), C(M,N)

PRINT *, "This example computes real matrix C=alpha*A*B+beta*C"
PRINT *, "using Intel(R) MKL function dgemm, where A, B, and C"
PRINT *, "are matrices and alpha and beta are double precision "
PRINT *, "scalars"
PRINT *, ""

PRINT *, "Initializing data for matrix multiplication C=A*B for "
PRINT 10, " matrix A(",M," x",K, ") and matrix B(", K," x", N, ")"
10    FORMAT(a,I5,a,I5,a,I5,a,I5,a)
PRINT *, ""
ALPHA = 1.0
BETA = 0.0

PRINT *, "Intializing matrix data"
PRINT *, ""
DO I = 1, M
DO J = 1, K
A(I,J) = (I-1) * K + J
END DO
END DO

DO I = 1, K
DO J = 1, N
B(I,J) = -((I-1) * N + J)
END DO
END DO

DO I = 1, M
DO J = 1, N
C(I,J) = 0.0
END DO
END DO

PRINT *, "Computing matrix product using Intel(R) MKL DGEMM "
PRINT *, "subroutine"
CALL DGEMM('N','N',M,N,K,ALPHA,A,M,B,K,BETA,C,M)
PRINT *, "Computations completed."
PRINT *, ""

PRINT *, "Top left corner of matrix A:"
PRINT 20, ((A(I,J), J = 1,MIN(K,6)), I = 1,MIN(M,6))
PRINT *, ""

PRINT *, "Top left corner of matrix B:"
PRINT 20, ((B(I,J),J = 1,MIN(N,6)), I = 1,MIN(K,6))
PRINT *, ""

20   FORMAT(6(F12.0,1x))

PRINT *, "Top left corner of matrix C:"
PRINT 30, ((C(I,J), J = 1,MIN(N,6)), I = 1,MIN(M,6))
PRINT *, ""

30   FORMAT(6(ES12.4,1x))

PRINT *, "Example completed."
STOP

END
```

Note

This exercise illustrates how to call the `dgemm` routine. An actual application would make use of the result of the matrix multiplication.

This call to the `dgemm` routine multiplies the matrices:

```CALL DGEMM('N','N',M,N,K,ALPHA,A,M,B,K,BETA,C,M)
```

The arguments provide options for how Intel MKL performs the operation. In this case:

`'N'`

Character indicating that the matrices A and B should not be transposed or conjugate transposed before multiplication.

`M, N, K`

Integers indicating the size of the matrices:

• A: `M` rows by `K` columns

• B: `K` rows by `N` columns

• C: `M` rows by `N` columns

`ALPHA`

Real value used to scale the product of matrices A and B.

`A`

Array used to store matrix A.

`M`

Leading dimension of array `A`, or the number of elements between successive columns (for column major storage) in memory. In the case of this exercise the leading dimension is the same as the number of rows.

`B`

Array used to store matrix B.

`K`

Leading dimension of array `B`, or the number of elements between successive columns (for column major storage) in memory. In the case of this exercise the leading dimension is the same as the number of rows.

`BETA`

Real value used to scale matrix C.

`C`

Array used to store matrix C.

`M`

Leading dimension of array `C`, or the number of elements between successive columns (for column major storage) in memory. In the case of this exercise the leading dimension is the same as the number of rows.

Intel MKL provides many options for creating code for multiple processors and operating systems, compatible with different compilers and third-party libraries, and with different interfaces. To compile and link the exercises in this tutorial with Intel® Composer XE, type

• Windows* OS: `ifort /Qmkl dgemm_example.f`
• Linux* OS, OS X*: `ifort -mkl dgemm_example.f`

Note

This assumes that you have installed Intel MKL and set environment variables as described in http://software.intel.com/en-us/articles/intel-mkl-111-getting-started/.

For other compilers, use the Intel MKL Link Line Advisor to generate a command line to compile and link the exercises in this tutorial: http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/.

After compiling and linking, execute the resulting executable file, named dgemm_example.exe on Windows* OS or a.out on Linux* OS and OS X*.

Optimization Notice

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804